They said Thursday that he should disavow such talk. Democratic state Rep. Jim Dunnam of Waco says talk of secession is anti-American and that some people associate it with racial division and the Civil War.
Perry's office did not immediately respond Thursday.
Answering a question from The Associated Press at an anti-tax rally Wednesday, Perry said he doesn't think Texas should secede. But he said the federal government was thumbing its nose at the American people and added, "who knows what might come out of that."